Motion Modeling In Subspace And State Estimation

Tracking is an important part in radar data processing.It refers to dealing with the measurements of the target appropriately,so that the random errors in the measurements can be suppressed effectively and the estimation of the target state can be maintained in real time.For Doppler radar,there are two main types of traditional target tracking methods:First,Model the target motion in cartesian space,and directly estimate the cartesian state of the moving target with the observations including Doppler measurement.The strong nonlinearity of the Doppler measurement is the difficulty and hotspot of such problems in the past decade.Second,Model the target motion in the observation coordinate system,so that the advantage of the linearity and Gaussian of the measurement equation is retained.However,the observed coordinate models used in such problems currently are approximate empirical models,which can not accurately reflect the true evolution law of the observation components over time.In order to solve these problems,the research on motion modeling in subspace and state estimation is carried out in depth in this paper.The main results obtained are as follows:1.For the strong nonlinearity of Doppler measurement,a tracking method for rationally using Doppler measurement to improve the estimation accuracy in direction cosine coordinate of phased-array radar is proposed.The converted Doppler is constructed by the product of range and Doppler,then the pseudo-state is constructed by the converted Doppler and its derivative,so that the strongly nonlinear Doppler information can be converted to linear pseudo-state subspace to be processed and the linear filter can be used to extract more velocity information from the Doppler measurement.At the same time,the converted position measurement and converted Doppler measurement as well as the mean,covariance,and cross-covariance of their converted errors in direction cosine coordinate are derived,and two linear estimators are constructed to extract pseudostate and cartesian state from converted Doppler measurement and converted position measurement,respectively.Finally,under the minimum mean squared error(MMSE)criterion,the outputs of the two estimators are statically fused to obtain the final target state estimate.Typical comparative simulation experiments show that the method proposed in this paper can effectively improve tracking accuracy and stability,especially in scenarios where the position measurement error is relatively large,the relative root mean squarederror(RRMSE)of the position and velocity estimated by the method proposed in this paper can be reduced by more than 30% compared to the sequential extented kalman filter(SEKF)and the unscented kalman filter(UKF).2.For the lack of accurate observed coordinate model,the target motion is modeled in range-Dopple subspace and the time evolution equation of range and Doppler is formulated.The state estimation method that directly extracts target range information and Doppler information using only range measurement and Doppler measurement is proposed,this builds the foundation for tracking and other applications in range-Doppler subspace.In this paper,the range-Doppler state vectors for three common motions constant velocity(CV),constant acceleration(CA)and constant turn(CT)are constructed by range,Doppler and dirivatives of the product of range and Doppler.Then the state equations corresponding to the three motions are derived by explicit substitutions according to the relationship between range-Doppler state and cartesian state.Finally,the UKF is used to extract target range-Doppler state from range measurement and Doppler measurement,the range estimation and Doppler estimation are thus obtained,and the filter initialization is derived by two-point differencing method where the correlation among the state components is handled properly.Typical comparative simulation experiments verify that the state estimation method based on the precise range-Doppler subspace model established in this paper can effectively improve the estimation accuracy of range and Doppler,compared with the range and Doppler estimated based on the empirical model,the RMSE can be reduced by more than 20% and 50%,respectively.3.Based on the work 2,the state estimation method using only range measurement is studied.The noise contained in range measurement can be filted using only range measurement,and the dynamic estimation of the parameters such as Doppler is realized at the same time.The filter initialization for three common motions CV,CA and CT is derived by two-point differencing method.Then for the large error problem of the twopoint differencing method in initializing high-order cases with only range measurement,a new initializaiton method based on the range-Doppler model is proposed.Through the range-Doppler state equation,the functional relationship between the range-Doppler state vector and the true range of several consecutive scans is constructed,then the state vector is initialized by replacing the true range with range measurement.The corresponding covariance is initialized by unscented transformation(UT)according to the nonlinear relationship between initial state vector and range measurement from several consecutivescans.Due to the consideration of the state equation constraint rather than simply using two-ponint differencing method for approximation,the new initialization method is more accurate,especially in the scenarios where target range changes nonlinearly with respect to time.Finally,the UKF is used to extract target range-Doppler state from range measurement,the range estimation and Doppler estimation are thus obtained.Typical comparative simulation experiments verify that the state estimation method using only range measurement is effective,and the proposed initialization method is more accurate than the two-point differencing method,the RMSE of range and Doppler estimated can be reduced by more than 30% and 50%,respectively.